please help me figure out whos getting the better of this?

[EricS31]

ok so me and a buddy were railing matusow, aba, etc play omaha...and we started prop betting the flops

person A
Wins $10 if no flop is seen
Wins $15 if first card on flop was a [img]/images/graemlins/heart.gif[/img]

person B
Wins $10 if [img]/images/graemlins/diamond.gif[/img], [img]/images/graemlins/club.gif[/img], or [img]/images/graemlins/spade.gif[/img] was first card on flop

whos getting the better of it in the long run?

[alphatmw]

wow a probability question i can answer (or at least try). going to just sloppily do some algebra, where P = probability of flop being seen

(P)*10 + 15*(1-P)*.25 = 10*(1-P)*.75
10P + (1-P)*3.75 = (1-P)*7.5
10P + 3.75 - 3.75P = 7.5 - 7.5P
13.75P = 3.75
P = 0.273

if they see the flop less than 27% of the time, you're getting the better of it. if more (which i would definitely assume so), you're getting the worse end.

[BruceZ]

[ QUOTE ]
wow a probability question i can answer (or at least try). going to just sloppily do some algebra, where P = probability of flop being seen

(P)*10 + 15*(1-P)*.25 = 10*(1-P)*.75
10P + (1-P)*3.75 = (1-P)*7.5
10P + 3.75 - 3.75P = 7.5 - 7.5P
13.75P = 3.75
P = 0.273

if they see the flop less than 27% of the time, you're getting the better of it. if more (which i would definitely assume so), you're getting the worse end.

[/ QUOTE ]

Correct algebra, but your interpretation is backward. In your equation, P is actually the probability of NOT seeing the flop, and P = 3/11. This means that person A has the best of it if there is NO flop more than 3/11 or 27.3% of the time, meaning that they see the flop less than 8/11 or 72.7% of the time. If there are 10 players, and each player sees the flop less than 13.4% of the time when they are not in the big blind, then person A has the best of it since (1-0.134)^9 > 3/11. This is reasonable if the game is tight enough.